A container closure of this general type is shown in Swiss Pat. No. 598,063 and U.S. Pat. No. 4,088,242. As shown therein, the closure has a desired separating line which has an inclined diaphragm portion parallel to the desired separating line which is formed with a groove-like cross sectional constriction the deformation thereof being able to compensate for deforming forces occurring in the diaphragm plane so that unintentional destruction can be avoided. However, it has been found that exceptional stresses applied to the container which can occur, for example, if the filled container drops on the floor with the lid raised and is compressed or crushed in the direction of the diaphragm plane, the deformation can be so great that, due to the inclined area, an adequate deformability is not present in the diaphragm plane and, instead, the diaphragm tears open at the line intended to be the desired separating line for opening the container.